Counting the Baskets

Revealed Coaching

I wanted to see how different one number player metrics lined up with how NBA coaches actually coach. So, I ran a series of simple linear regressions comparing the score on various player metrics to minutes player per game last year.  Since each metric takes a slightly difference approach, it could tell us a bit about what NBA coaches value. The idea is similar to a Ari Caroline piece over at Wages of Wins last year comparing how their metric, Wins Produced, stacked up with minutes. Here I have added PER, ASPM, xRAPM and Win Shares.

The results are very preliminary but too interesting not to share. Among the caveats are that currently the WP number is a a three year average while the others are for current the year.  Though  I ran the 2012-2013 Win Produced numbers on a slightly different data set and got very similar results.  Also, the two year ASPM actually did better than the single year, suggesting, sensibly, I think, coaches have prior beliefs coming into the season and adjust somewhat slowly to unexpectedly good or poor performances.

In any case, in the table below I have R squared numbers, or,  goodness of fit, from each simple regression I ran.

	R2 Player Metric and MPG
	WP48	WS	PER	ASPM	xRAPM	2 Yr ASPM
PG	0.335	0.262	0.441	0.494	0.359	0.535
SG	0.093	0.148	0.345	0.388	0.266	0.459
SF	0.095	0.068	0.215	0.348	0.311	0.391
PF	0.004	0.057	0.325	0.247	0.214	0.213
C	0.145	0.144	0.394	0.335	0.348	0.339
ALL	0.088	0.101	0.298	0.333	0.24	0.34

 

The yellow highlighted background cells are the highest correlation for that metric.  Astute observers may notice a pattern; all of the stats agreed most with the minutes allocations given out at the Point Guard position. This supports the idea that the Point is the best defined and understood position in the game right now. Since I made the claim that's how I am going to interpret it.

The red highlighted lines are the position each stat agreed least with the minute allocation. In this case, the Power Forwards are the opposite of the Point Guards where each metric save PER had their lowest fit on that position.  For PER the worst fit was at small forward.

Looking for the best fitting metric by each position, Daniel Myers' ASPM in both the single year and two year weighted average correlated the best to minutes assigned for Point Guards, Shooting Guards, and Small Forwards. While John Hollinger's PER fit the best for both Power Forwards and Centers.

By the way, my unofficial outlier awards goes to Ben Gordon, whose game all of the metrics hate and yet still managed to see 21 minutes a game.  And the hyper efficient Jeremy Evans, loved by all except xRAPM and Ty Corbin getting just under six minutes a game.

So what does that say about the advanced metrics and about coaches?

Not all of the metrics are created equally in terms of preditive ability (or retrodictive ability). A blog called the Sports Skeptic did a retrodictive test a while ago, using the advanced stat scores from the year before applied to the playing minutes the next year. The author found that of the ones I am looking at PER had the lower predictive abilities.  But confusingly ASPM had one of the highest predictive abilities.

So, coaches can judge guard's abilities, other than Ben Gordon, but not bigs? Probably too early to say that.

Also, I am currently working on some multiple regressions, which will include more years.  So far, the plus/minus stat xRAPM has come in as a positive combination with each of the other box score based metrics, the next step will be to break up plus minus into its offensive and defensive components to  see if my hunch that it is the defensive side of xRAPM that is adding value is correct.  Also, games played, which I included as an indication of injuries, has come in has a positive contributor improving each metric's score.

As for the metrics, it looks like analytics movement still has a ways to go in gaining actual influence, Wins Produced and Win Shares in particular.

Great, and Not-So-Great, Expectations

Instead of projecting the Celtics record, which I plan to do, I thought I would start by evaluating the Celtics roster overall.  Projecting wins means projecting minutes, which is particularly tough on a team with turnover and a new coach.

The approach I took was to compare how the advanced metrics view the C's roster compared to a replacement player in the NBA. This gives a partial idea of how good the players look over the entire roster and gives a range of their expected value. Take a look at the brief explanation of the metrics used  in the extended Grantland style footnote**, or go here for Evan Zamir's primer.

I used 'replacement player' rather than 'average player' because when I looked at the stats I found that most players have below average production. That's because the best players on most teams get more minutes, so the production numbers are skewed upward. Replacement player also gives one an idea of the value you could expect with a vet minimum type player. The level I chose is also at about the rating of players in the 25th percentile in the NBA.

All that said, any player with less than 4 wins over replacement has below average production.

So, below is each of the metrics ratings comparing playing that player playing starter level minutes, 36 minutes for every game, to a replacement level player win terms of added or subtracted wins and losses.

 

Name	xRAPM Wins Compared to Replacement Player per 36	ASPM Wins Compared to Replacement Player per 36	Win Shares Compared to Replacement per 36	Wins Produced Compared to Replacement per 36	EZPM Wins Compared to Replacement player per 36	Average Wins Over Replmnt Player	Range
Avery Bradley	2.7	0.6	2.6	0.2	-2.8	0.7	5.5
Brandon Bass	0.8	2.7	5.7	3.8	-4.2	1.8	9.8
Courtney Lee	1.9	3.7	3.8	5.2	3.8	3.7	3.3
Gerald Wallace	8.0	6.7	4.1	6.6	5.4	6.2	3.9
Jared Sullinger	4.4	5.2	9.0	7.2	6.0	6.4	4.7
Jeff Green	2.1	3.1	4.9	2.0	6.4	3.7	4.4
Jordan Crawford	-0.2	-1.0	1.8	-2.0	-7.0	-1.7	8.8
Keith Bogans	-1.5	0.0	-0.2	3.8	-4.8	-0.6	8.6
Kelly Olynyk	3.6	4.0	2.2	1.6	4.0	3.1	2.4
Kris Humphries	3.6	0.4	5.8	10.5	2.8	4.6	10.1
Marshon Brooks	-1.9	0.4	2.2	2.6	6.0	1.8	7.9
Phil Pressey	-0.3	-0.3	-1.0	-1.5	0.0	-0.6	1.5
Rajon Rondo	11.0	9.0	5.8	12.6	10.5	9.8	6.8
Vitor Faverani	1.1	1.1	1.3	2.1	1.1	1.4	0.9

 

A couple things come out here:

• Avery Bradley- The metrics don't like his game too much, in part because he didn't play very well last year on offense. xRAPM, which as a plus/minus stat, is probably the best at accounting for defense, likes him the best.
• Gerald Wallace- All the metrics like him. I think fans are under valuing him because he is over payed and his contract is too long. Over payed does not equal can't play. If he bounces back, he could be valuable to a contender at the deadline.
• Jared Sullinger- The metrics think he earned his starting minutes. He could be the most fun player to watch this year if the back is indeed healthy.
• Jeff Green doesn't do great or too bad. The metrics don't know which Green will show up any more than anyone else does.
• Crawford and Bogans- None of the metrics like them particularly, and they're rated below replacement level overall.
• Kris Humphries is the most controversial according to the metrics with a range of 10 wins. Win's Produced, which is a rebound heavy metric, likes Humphries a lot.
• Rajon Rondo- Not surprisingly, Rondo is the key to the season. Coach and locker room drama aside, Rondo's production is the key to being competitive for this team at all with a 10 win swing from Rondo to a replacement level point guard, which about what the team has as options.
• Faverani, Pressey, and Olynyk are based on a combo of the Wages of Wins projections based on their Euro or NCAA numbers and my selection of rookie 'comps' for other metrics.  In other words, semi-educated guesses.

So, that's it there're talent on the team, but at this point one star and some potential.

** xRAPM- This is an advanced adjusted plus minus stat. The version here comes from Nathan Walker at Basketball Distribution. He used three years of data and an aging factor.

ASPM- This a box score based stat developed by Daniel Meyers. I like this one, in part because it did the best in an independent study in terms of both consistency and predicting, though only narrowly. It's also pretty intuitive. I used two years of ASPM ratings weighted by minutes and giving more weight to last year than the prior year. I also added an aging factor.

Win Shares- Box score stat developed by Justin Kubatko based Dean Oliver's 'four factors'. I used two years of ratings and an aging factor.

Wins Produced- Box score stat developed by Dave Berri that loves rebounds. I used a projection by Arturo Galleti at Wages of Wins, using three years of ratings weighted by minutes and an aging factor.

EZPM- Evan Zamir's Play by Play data based stat. This one is sort of complicated, but it's the only one using play by play data. I only had one year of data and applied an aging adjustment.